Hash, Thorough, Through, Haphazard, Which...
aches
heels heeds hiest
otherashesachesashenochreaphid
anthillanthraxauthorsbashingbathingbathmatbathtubboyhoodcashingcushiondashingdishingenchainenthralfashionfathersgushinginchingjoshinglashingmachinemashingmothersmushingnoshingnothingonshorepushingreshaperethinkrushingunchainurchinswashingwishingwithers
that what when thus then then than
hurrah
The word is with w-it-h\Other 4 letter words with it in the middle:bitecitecityfitshitskitskitelitemitepitsritesitesitswitszits
some 5 letter words that starts with "h" are heart and horse
which
house
trash
Shush.
beach